Dealing with degeneracies in automated theorem proving in geometry: A zero-dimensional approach

• Zoltán Kovács ^[3] ; Tomas Recio ^[1] ; Tabera, Luis F. ^[2] ; M. Pilar Vélez ^[1]
  1. [1] Universidad Nebrija

     Universidad Nebrija

     Madrid, España

     
  2. [2] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
  3. [3] The Private University College of Education of the Diocese of Linz

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• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor , Philippe Giménez , Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo , Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 111-114
• Idioma: inglés
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  • In the presentation we will start by reporting, using various examples to present the current development in GeoGebra of geometric automated reasoning tools by means of computational algebraic geometry algorithms. "Ve will then introduce andanalyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. The first is to work with the saturation of the hypotheses ideal with respect to the ring ofgeometrically independent variables, as a way to globally handle the statement over all non-degenerate components. The second is to consider the reformulation of the given hypotheses ideal considering the independent variables as invertible parameters, exploiting the specific properties of this zero-dimensional case to analyze the truth of the statement over each non-degenerate component.